Consequences of increasing the length of the iron core in electric motor 7

[EngRepair]

Hypothetical, theoretical question about electric motors.
Let's say we have a fully functional three-phase squirrel-cage LV motor.
Let's imagine we made another one with exactly the same geometry of stator and rotor lamination, exactly the same winding (turns/coil, wire size, pitch, etc...).
The only difference should be the length of the stator and rotor cores.
Let's say the length is increased by 10%.
Also, the motor load will remain the same as before.
What changes will this cause in terms of hp, torque, rpm, FLA, NLA, efficiency, and power factor?
It would be greatly appreciated to hear some expert opinions.

 

[edison123]

10% increase in core length = 10% increase in output, torque, NLA, FLA and iron loss.

No. of turns must change proportionately for the above parameters.

Speed no change unless you rewind for different no. of poles.

Efficiency and pf will not change much.



Muthu

http://www.edison.co.in

 

[electricpete]

LPS to edison. Just to talk it through:

No. of turns must change proportionately for the above parameters.

I agree decreasing turns by roughly 10% would keep the flux density constant.
V ~ N * B * A
In order to keep V and B constant than N must change by the inverse of the ratio that A increases.

10% increase in core length = 10% increase in output, torque, NLA, FLA and iron loss.
Efficiency and pf will not change much.

All of that sounds about right to a reasonable approximation given we have reduced N to keep B the same.

rpm

Inherent in previous answers, we assumed the same number of poles but we also assumed the rotor length was increased by the same 10% as the stator. So the bar resistance will increase by 10%. The end ring resistance will not increase at all. So equivalent circuit parameter R2 will increase by some factor between 0 and 10%... (for the sake of discussion let's say swag 5%). Slip at a given power is proportional to that parameter R2. So slip at a given power will increase by that same factor (swag 5%)

edit - it's a little more complicated than what I described above. I discussed above R2 considering the rotor only, so referenced to the rotor side of the circuit. But the relevant R2 for the for the purpose of predicting performance in the way I did ("slip for a given power is proportional to R2") would be referenced to the stator. We changed the stator turns, which affects the ratio we would use to translate R2 from the rotor side to the primary side.

Also, the motor load will remain the same as before.

Motor load is not a characteristic of the motor. Motor will (roughly speaking) match the connected load, whatever it that is, just as long as it's within the motor capability. Therefore your comment that motor load will remain the same is meaningless.... unless you are suggesting some other change to take advantage of the longer core by changing some other parameter to optimize cost or other parameters... but that's a lot more nebulous and you'd have to explain a lot more what you're looking for.


=====================================
(2B)+(2B)' ?

 

[EngRepair]

Unfortunately, I did not receive the expected response.
If you read carefully what I wrote, the question is clear and there is nothing nebulous about it.

No. of turns must change proportionately for the above parameters.

Please read my post again.

Let's imagine we made another one with exactly the same geometry of stator and rotor lamination, exactly the same winding (turns/coil, wire size, pitch, etc...).
The only difference should be the length of the stator and rotor cores.

Therefore your comment that the motor load will remain the same is meaningless.

What is not clear?
The new motor would work on the same machine and the same load.

 

[edison123]

Ditto.

Muthu

http://www.edison.co.in

 

[electricpete]

Unfortunately, I did not receive the expected response.
If you read carefully what I wrote, the question is clear and there is nothing nebulous about it.

....No. of turns must change proportionately for the above parameters.

V / N ~ B * A = B L W (where L is coil length and W is width as in span. )

If you insist to keep turns per coil the same and all other coil parameters the same, then the left side is constant, W is constant, and the product (B L) would have to remain constant. That means flux density B will decrease by the same fraction that the L increased (10%).

T = R N I L B cos(theta) where theta is angle between the flux and current which is roughly constant.
Since the product of (B L) is constant, then I think you can reach a given torque with the same current as before.

The stator and rotor resistance will increase. The component of resistances associated with the slot will increase by 10%. The component associated with the endwindings / endrings increases by 0%. The total resistance increases somewhere between 0 and 10%, let's say 5%

So for a given torque load:
[ol 1]
[li] The current remains the same[/li]
[li] I^2*R losses increase due to increasing R[/li]
[li] core losses decrease due to decreasing B.[/li]
[/ol]
In terms of efficiency at a given load, i'm not sure off the top of my head which factor we'd expect to dominate: 2 or 3. It may be the the 3rd factor (which is relatively load independent) dominates at low loads and the 2nd factor (which increases with load) dominates at high loads.

in terms of rpm, I'll stick with my comments from before (the increasing R2 will cause increasing slip for a given load). You could go back again and question why i looked at torque load instead of hp load, but I'll assume any fractional change in speed is much smaller than the other changes we're looking at.


=====================================
(2B)+(2B)' ?

 

[edison123]

pete - Increasing the core length with the same no. of turns will reduce the flux density and thus the motor torque.

A knowledgeable design engineer would never do the same no. of turns after stripping the winding to add 10% core - which in itself is an impractical and expensive proposal - and then not do the new winding for the increased core length

Muthu

http://www.edison.co.in

 

[electricpete]

A knowledgeable design engineer would never do the same no. of turns after stripping the winding to add 10% core

I agree 100%. I only addressed the constant turns requirement after OP reiterated it (hence why i said "if you insist...") At this point it's an academic excercize.

increasing the core length with the same no. of turns will reduce the flux density and thus the motor torque.

I assume we are talking about a constant current.
Yes the flux density decreases and that factor tends to decrease torque corresponding to a given current.
BUT length increases which tends to increase torque corresponding to a given current. It seems like you're ignoring that length piece of the torque equation.
Those two effects oppose each other
if length were irrelevant to torque production for a given current, turns, flux density radius etc, then everyone would save money and build cores as short as they could.

T = R N I L B cos(theta)
where T is torque, R is radius of airgap, N is number of turns in entire winding, I is current, L is length of slot section, B is airgap flux density, cos(theta) is the electrical angle between the main B and I waves (which can be assumed roughly constant).
Assuming I is constant and N is constant, then when L increases, B decreases and the product of (L B) stays constant (neglecting 2nd order effects and non-linearities), and T remains constant.


=====================================
(2B)+(2B)' ?

 

[Gr8blu]

EngRepair: As a designer - simply adding core length (to both stator and rotor) and not changing anything else, including the process to be driven, results in a motor that operates at a lower flux density. At lower flux densities, the core losses tend to be a bit less, but that is offset by having more resistance in a given circuit (same number of turns and cross-section, longer distance) and possibly a bit higher temperature rise (original fan design may not be adequate to overcome the additional pressure drop from the longer core). Net effect? It's a wash. HP capability is one thing, HP used to drive the process is another. If you're asking about how much the process will draw with the longer core - the answer is THE SAME AMOUNT as before. This is because the PROCESS has not changed. If you're asking whether you could load the longer core more, then the answer is yes - although probably not the full 10% unless you also make a lot of other changes (turn count, coil pitch, fan design, etc.) to the design to optimize the new geometry. Bottom line: changes to efficiency and power factor are going to be (relatively) unnoticeable for the normal run of machine outputs. You might be able to measure something worthwhile for a machine rating in the hundreds of MW. Torque is going to be a wash too, for the reasons noted above by another poster.

Converting energy to motion for more than half a century

 

[edison123]

pete

Same turns with more core means the current rating remains the same (since no change in copper area) and hence no change its part on torque while the lower flux density (due to same turns) will lower the torque.

Reduced turns with more core means same flux density and higher current (due to copper area in fewer turns), higher torque, higher HP etc.

Those two effects oppose each other if length were irrelevant to torque production for a given current, turns, flux density radius etc, then everyone would save money and build cores as short as they could.

is meaningless.

Muthu

http://www.edison.co.in

 

[waross]

All the factors and dimensions in a motor are optimized for efficiency, cost of production and cost of running.
If one dimension or parameter is changed without changing any others, the resulting performance will, in most cases, be less than before.

--------------------
Ohm's law
Not just a good idea;
It's the LAW!

 

[electricpete]

increasing the core length with the same no. of turns will reduce the flux density and thus the motor torque

I assume we are talking about a constant current.
Yes the flux density decreases and that factor tends to decrease torque corresponding to a given current.
BUT length increases which tends to increase torque corresponding to a given current. It seems like you're ignoring that length piece of the torque equation.

Those two effects oppose each other
if length were irrelevant to torque production for a given current, turns, flux density radius etc, then everyone would save money and build cores as short as they could.
T = R N I L B cos(theta)
where T is torque, R is radius of airgap, N is number of turns conductors in entire winding, I is current, L is length of slot section, B is airgap flux density, cos(theta) is the electrical angle between the main B and I waves (which can be assumed roughly constant).
Assuming I is constant and N is constant, then when L increases, B decreases and the product of (L B) stays constant (neglecting 2nd order effects and non-linearities), and T remains constant.

You'll note i said "I assume we are talking about a constant current" and "that factor tends to decrease torque corresponding to a given current."

EDITED TO DELETE:If we further assume roughly constant speed (which is reasonable since fractional change in slip gives much smaller fracitonal change in speed) then it means assuming roughly the same horsepower and the question boils down to whether the motor has more or less losses or is less or more efficient at a given load when we increase length and keep turns the same. Gr8Blu has weighed in with roughly the same assertion as me: "the core losses tend to be a bit less, but that is offset by having more resistance in a given circuit... Net effect? It's a wash."

If you have in mind something different than comparing torque at the same current, then please clarify the parameters of your assertions.

Same turns with more core means the current rating remains the same (since no change in copper area) and hence no change its part on torque while the lower flux density (due to same turns) will lower the torque.

Yes, lowering flux density would decrease torque for a given current IF length were constant.
And increasing length would decrease torque for a given current IF flux density were constant.
When we have both B and L changing in opposite directions, we cannot as easily predict the result...

I have already mentioned the equation:
T = R N I L B cos(theta)
...which plainly shows us the role that the variables play (including both B and L), and supports my assertions.

In section 12.3 of the attachment, that equation is "derived" from the Lorentz force equation for force on a current-carrying conductor in a magnetic field. (As an unnecessary aside, it turns out the derivation relies on two false assumptions; 1 - the torque producing force acts primarily on the conductors and 2 - the conductors are exposed to the airgap flux density; but in this particular case, two wrongs do indeed make a right, i.e. if we use airgap flux density for B then the equation does indeed give the right answer as confirmed by analysing example motor in 12.4.1. and comparison to a textbook equation in 12.4.2). Feel free to ignore my parenthetical comments, they are not essential to the discussion. The equation above is well confirmed and well known (some forms of the equation may have constant factors which will not change the conclusion See Note 1). If you have some alternate equation for torque that includes relevant variables including B, L, I to support your assertion, then please post it.

Note 1 - In section 12.4.2, my equation matches the Ref 9 textbook equation except for the constant winding factor Kdp. Kdp does not appear in my equation due to simplifications in modeling of the current distribution. However Kdp would be a constant under the scenario of consideration and does not affect the conclusion.

https://files.engineering.com/getfi...f-ae6e48385ca0&file=TheLongVersion091207_.pdf

 

[edison123]

pete

I have already explained both the theory and practice. Do not have time to get into theoretical weeds with you.

I reiterate with no corresponding turns correction for increased core length, there will be a torque reduction and there is no 'wash' with current torque, since current increase is impossible with same no. of turns.

Muthu

http://www.edison.co.in

 

[electricpete]

I have already explained both the theory and practice.

You have not explained your position well. Maybe there is a valid position you are trying to articulate, but I cant figure out any context (what are we holding constant) in which your assertions would be logical. I have stated my own assumptions. I'm pretty sure we must be talking about different things.

Do not have time to get into theoretical weeds with you.

Let me add some arrows to the equation so it's very simple to talk about the following equation:

T = (R→) (N→) (I→) (L↑) (B↓) (costheta→)

That equation explains my statements. If you don't agree, then I have to ask two questions:
[ol 1]
[li]What makes you think (B↓) always wins over (L↑)? (if we start and remain in the linear range of B vs H then the product B L would be constant and it's a wash. if we start far into saturation then increasing length wouldn't change B much and L would win!)[/li]
[li]Do you have an alternate expression for torque involving these variables?[/li]
[/ol]

I reiterate with no corresponding turns correction for increased core length, there will be a torque reduction..

Disagree.

... and there is no 'wash' with current torque, since current increase is impossible with same no. of turns.

I didn't claim a current increase would occur, I assumed we were comparing performance at a given current.

 

[waross]

I reiterate with no corresponding turns correction for increased core length, there will be a torque reduction and there is no 'wash' with current torque, since current increase is impossible with same no. of turns.

Doesn't current increase with increased slip?
Do we get an offsetting increase in torque from the longer length?
Possibly the breakdown torque may be less.


--------------------
Ohm's law
Not just a good idea;
It's the LAW!

 

[electricpete]

To allevaite any potential confusion about what scenario I'm addressing, I have to point out that there was a subtle change in my assumptions between my earlier post 4 Mar 23 21:10 (where I was addressing constant torque) and the next 2 posts on 7 Mar 23 14:21 and 7 Mar 23 14:21 (where I was assuming constant current). I started with constant torque in my earlier post 4 Mar 23 21:10 because it seemed like a logical comparison. I changed to constant current in response to edison's post 5 Mar 23 15:35 where he said increasing length would decrease motor torque.... because I couldn't argue against a change in motor torque by simply assuming constant motor torque (that would be somewhat circular logic), so instead i created the equivalent assumption of constant current. Under what circumstances are the two assumptions equivalent? ... The constant current and constant torque assumptions are equivalent if we are in the linear range of the magnetic curve where our scenario (increasing length without changing anything else) results in a constant product of B times L. With constant product of B times L then constant torque and constant current are equivalent assumptions: T = (R→) (N→) I (L B→) (costheta→)

If we make a further reasonable assumption of negligible change in speed (fractional change in speed is much less than fractional change in slip), then the constant torque assumptioin equates to constant load power and the question boils down to whether the motor has more or less losses or is less or more efficient at a given load when we increase length and keep turns the same. Gr8Blu has weighed in with roughly the same assertion as me: "the core losses tend to be a bit less, but that is offset by having more resistance in a given circuit... Net effect? It's a wash."

That's a little convoluted but i wanted to make it clear what assumptions are behind everything that i said. In contrast, I cannot say it's clear to me what assumptions are behind edison's assertion that torque decreases.

 

[EngRepair]

In fact, this is not a purely hypothetical scenario.
One of our customers brought a submersible water pump to our service for repair, which worked successfully for a long period of time.
At the same time, the customer had the intention of replacing it with a new spare pump from their warehouse (same manufacturer, same nameplate, but the length of the motor is approximately 10% higher).
They contacted the manufacturer who confirmed that it is the same motor, with the exactly same winding data but with a longer core length, and that they can use it without any worries as a replacement. The manufacturer did not provide an explanation for the longer core.
The customer was suspicious of the manufacturer's assurance that the replacement pump would work without issue and asked us for advice.
As far as I know, a longer core length with the same winding details leads to a reduced air gap flux density and consequently lower torque and HP.
Thus if the new motor will be loaded with the same load as the old one, an overcurrent will occur.
Therefore, my recommendation was: do not use the new motor in the same place and under the same load.
I'll see what they going to do.
Bear in mind that the usual practice in submersible motor production is the use of the same stator and rotor laminations for the whole HP range,(for the particular diameter of pumps, for example, 6 or 8, or 10 "). The only difference is in the length of the core.

 

[electricpete]

> As far as I know, a longer core length with the same winding details leads to a reduced air gap flux density and consequently lower torque and HP.

No, that would not be my conclusion. My conclusion is that it's unknown, but probably a wash. I'm going back to my comments 4 Mar 23 21:10

V / N ~ B * A = B L W (where L is coil length and W is width as in span. )

IF we assume magnetic linearity
[ul]
[li]The product B L is constant. That means flux density B will decrease by the same fraction that the L increased (10%).[/li]
[li]T = R N I L B cos(theta) where theta is angle between the flux and current which is roughly constant.[/li]
[li]Since the product of (B L) is constant, then I think you can reach a given torque with the same current as before.[/li]
[li]The stator and rotor resistance will increase. The component of resistances associated with the slot will increase by 10%. The component associated with the endwindings / endrings increases by 0%. The total resistance increases somewhere between 0 and 10%, let's say 5%[/li]
[li]So for a given torque load:[/li]
[li]The current remains the same[/li]
[li]I^2*R losses increase due to increasing R[/li]
[li]core losses decrease due to decreasing B.[/li]
[li]In terms of efficiency at a given load, i'm not sure off the top of my head which factor we'd expect to dominate: 2 or 3. It may be the the 3rd factor (which is relatively load independent) dominates at low loads and the 2nd factor (which increases with load) dominates at high loads.[/li]
[li]in terms of rpm, the increasing R2 will cause increasing slip for a given load. Slightly lower speed at the same torque means slightly lower power, but it's a very small effect ... if slip increases by 5% the decrease in speed is much lower. Let's say sync speed 1000rpm, original slip 40rpm, new slip 42rpm, original speed 960rpm, new speed 958rpm, speed decrease 2/960 = 0.2%. That was assuming a large slip to begin with (4%)... if you had a smaller slip than the speed decrease is even less. Even f we stick with 4% initial slip than this whole speed thing gives you a derating of 0.2% horsepower... irrelevant in the bigger scheme of things imo.[/li]
[/ul]
If we don't assume magnetic linearity, the product of L B is going to increase (rather than remaining constant) as we increase L... and that favors the lengthened core to perform even better.

There is a minor effect on flux density not considered before that X1 is going to increase which might decrease the flux density at full load slightly (that effect is not considered in the initial equation V / N ~ B * A = B L W). It's a relatively small effect. As a first swag L is typically 0.1pu but it doesn't cause a 0.1pu drop in magnetizing branch voltage because the full load current is closer to resistive than inductive.

All in all I think I'd feel comfortable to keep the rating and FLA and efficiency estimate the same for most purposes but no matter how you slice it, it's a rough estimate in comparing competing effects. If you give more details about the motor it may be possible to improve estimates somewhat. For example from full nameplate (and preferably performance data) the equivalent circuit parameters could be estimated. Then for L1 we could say it increases by some fraction between 0 and 10% (I'd have to think a little more about that fraction) and then try to estimate what the effect on full-load B would be. No doubt any number we come up with will be a rough estimate though... it's a separate question how much confidence you want in your answers and the uncertainty around them. If it's a super critical application with no room for error and you don't have time or resources for detailed analysis, then it could certainly be a conservative approach to assume a 10% derating (undoubtedly overconservative for most purposes, but conservative nonetheless).

 

[waross]

They contacted the manufacturer who confirmed that it is the same motor, with the exactly same winding data but with a longer core length

That statement is suspect.
Did it come from a design engineer or from a sales engineer?
It may mean that the connections are identical.

Let's look at it from two ways.
1. Torque per unit length: Less force to generate torque per unit length, but a corresponding increase in length.

2. An actual reduction in overall torque of 10%.
Assume a 1760 RPM motor. The slip at full load is 40 RPM. 10% less slip means 4 RPM less speed.
The 1760 RPM motor may now be actually a 1756 RPM motor.

Why the change?
Lower flux density may make the motor better able to accept over-voltages.
Will the lower flux density result in more torque and faster acceleration when the core saturates during starting?

And a comparison:
208 Volts versus 240 Volts on the same motor. 13% change.


Don't forget that motor characteristics are not constant but are dynamic.
Speed, slip, torque, current; All are interdependent and change with changing load.

I would not hesitate to use the new motor. The manufacturer has much more information available on the effect of the change then do we.

We have had a discussion concerning what we thought was a theoretical change.
Now we find that we are second guessing a design change.

You have had conflicting replies from a number of motor experts.
I respect the experience and technical knowledge of the experts, even though they disagree.
The experts who have responded represent several hundreds of years of experience.

Even though the spare motor may be off warranty, there will be many similar motors still under warranty.
Had the manufacturer experienced problems with the new design , they would have warned your customer off and suggested an alternate solution.
AND
More iron is generally better.

--------------------
Ohm's law
Not just a good idea;
It's the LAW!

 

[edison123]

pete

Let me simplify this further for you.

Torque is proportional to the product of flux density and current in any dc/ac motor.

With more core length and with same no. of turns, flux density will be decreased and current cannot go up without exceeding original current density (Amp/sq mm). Hence, the torque will go down since the current is same and flux density is lower.

The length you keep talking about is already accounted for in the flux density/emf equation.





Muthu

http://www.edison.co.in